-16t^2+24t+40=0

Solution for -16t^2+24t+40=0 equation:

Simplifying
-16t2 + 24t + 40 = 0

Reorder the terms:
40 + 24t + -16t2 = 0

Solving
40 + 24t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8'.
8(5 + 3t + -2t2) = 0

Factor a trinomial.
8((5 + -2t)(1 + t)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(5 + -2t)' equal to zero and attempt to solve:

Simplifying
5 + -2t = 0

Solving
5 + -2t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -2t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2t = 0 + -5
-2t = 0 + -5

Combine like terms: 0 + -5 = -5
-2t = -5

Divide each side by '-2'.
t = 2.5

Simplifying
t = 2.5
Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0 + -1
t = 0 + -1

Combine like terms: 0 + -1 = -1
t = -1

Simplifying
t = -1
Solution
t = {2.5, -1}